*Acta Math. Acad. Paed. Nyíregyháziensis*

15 (1999), 35-40

`www.bgytf.hu/~amapn`

# On the limit of a sequence

**Z. László and Z. Vörös**

### Abstract:

The object of this article is to examine the sequence

well known from probability theory. We prove that the sequence is bounded,
strictly monotonously decreasing, and The last two statements are proved by analytical
means. Finally, a modification and a generalization of (*an*) will
be mentioned, and the sketch of a second analytical proof for the original
limit will be given.

*Mathematics Subject Classification.* 26A12, 26A42, 40A05.

*Key words and phrases. *Limit,
probability, analytical means.